Corpus ID: 119619691

Order-Preserving Freiman Isomorphisms

@article{Amirkhanyan2018OrderPreservingFI,
  title={Order-Preserving Freiman Isomorphisms},
  author={G. Amirkhanyan and A. Bush and E. Croot},
  journal={Integers},
  year={2018},
  volume={18},
  pages={A8}
}
  • G. Amirkhanyan, A. Bush, E. Croot
  • Published 2018
  • Mathematics, Computer Science
  • Integers
  • An order-preserving Freiman 2-isomorphism is a map $\phi:X \rightarrow \mathbb{R}$ such that $\phi(a) < \phi(b)$ if and only if $a < b$ and $\phi(a)+\phi(b) = \phi(c)+\phi(d)$ if and only if $a+b=c+d$ for any $a,b,c,d \in X$. We show that for any $A \subseteq \mathbb{Z}$, if $|A+A| \le K|A|$, then there exists a subset $A' \subseteq A$ such that the following holds: $|A'| \gg_K |A|$ and there exists an order-preserving Freiman 2-isomorphism $\phi: A' \rightarrow [-c|A|,c|A|] \cap \mathbb{Z… CONTINUE READING

    Topics from this paper

    References

    SHOWING 1-8 OF 8 REFERENCES
    On distinct consecutive differences
    • 8
    • PDF
    On Double 3-Term Arithmetic Progressions
    • 4
    • PDF
    On the Bogolyubov–Ruzsa lemma
    • 115
    • PDF
    A New Proof of Szemerédi's Theorem for Arithmetic Progressions of Length Four
    • 396
    • Highly Influential
    • PDF
    A course in convexity
    • A. Barvinok
    • Mathematics, Computer Science
    • Graduate studies in mathematics
    • 2002
    • 696
    • PDF
    The structure theory of set addition revisited
    • 54
    • PDF
    Additive Combinatorics. Cambridge Studies in Advanced Mathematics vol. 105
    • 2006
    A statistical theorem of set addition
    • 129
    • Highly Influential